Previous studies have quantified the longitude gradients in E × Bdrift associated with the four-cell tidal structures and have confirmed that these sharp gradients exist on a day-to-day basis. For this paper, we incorporate the Ion Velocity Meter (IVM) sensor on the Communications/Navigation Outage Forecasting System satellite to obtain the daytime, verticalE × B drift velocities at the magnetic equator as a function of longitude, local time, and season and to theoretically calculate the F region ion densities as a function of altitude, latitude, longitude, and local time using the Global Ionosphere Plasmasphere model. We compare calculated ion densities assuming no longitude gradients in E × Bdrift velocities with calculated ion densities incorporating the IVM-observedE × Bdrift at the boundaries of the four-cell tidal structures in the Peruvian and the Atlantic longitude sectors. Incorporating the IVM-observedE × B drift velocities, the ion density crests rapidly converge to the magnetic equator between 285 and 300°E geographic longitude, are absent between 300° and 305°, and move away from the magnetic equator between 305° and 340°. In essence, the steeper the longitude gradient in E × B drifts, the steeper the longitude gradient in the equatorial anomaly crest location.
 It is well known that the production and loss of ions and electrons in the Earth's ionosphere comes from solar EUV radiation and the loss of O+ ions in the F region is by charge exchange with N2 and O2 followed by recombination with electrons. The transport of ionization is through plasma ambipolar diffusion parallel to B, the component of the neutral wind velocity parallel to B and E × B drift velocity perpendicular to B [Hanson and Moffett, 1966; Anderson, 1973]. In the equatorial region, E × B drift velocities are generally upward during the daytime and downward at night. The combined effect of upward E × B drift perpendicular to B and downward diffusion parallel to B by gravity and plasma pressure gradient forces create crests in ionization at ±15 to 18° dip latitude known as the equatorial anomaly.
 More recently, Immel et al. presented evidence that a four-cell, longitudinal pattern existed in FUV (135.6 nm) intensity obtained from the IMAGE satellite during March–April 2001. They attributed the four-cell pattern in airglow-inferred Nmaxvalues at the crests of the equatorial anomaly to a four-cell pattern in daytime, verticalE × B drift velocities associated with the diurnal, eastward propagating, nonmigrating wave number 4 (DE3) tidal mode [Hagan and Forbes, 2002]. The authors could not rule out the fact that the four-cell pattern could have been produced by a four-cell pattern in the prereversal enhancement (PRE) since the IMAGE observations were at night. A subsequent paper byEngland et al. , however, established that the four-cell pattern was observed by CHAMP satellite in situ electron densities at 1200 LT.
Scherliess et al. also observed the four-cell longitude pattern in TOPEX/TEC observations. The TOPEX/Poseidon satellite flew at 1336 km and incorporated a dual frequency altimeter operating at 13.6 GHz and 5.3 GHz to observe ocean surface height. Scherliess et al. binned the TEC observations between 1992 and 2005 for quiet days into Equinox, June solstice and December solstice periods by local time. The 1200–1600 LT period clearly displayed the four-cell pattern that had been observed by other techniques, previously.
 The Communications/Navigation Outage Forecasting System (C/NOFS) Ion Velocity Meter (IVM) E × B drift velocities presented in this paper are meridional ion drifts, perpendicular to B and in the plane of the magnetic meridian, measured with an accuracy of 2 m/s and a sensitivity of 1 m/s [de La Beaujardière et al., 2004]. Recently, Araujo-Pradere et al.  examined the longitude gradients in daytime, vertical E × Bdrift velocities near the boundaries of the four-cell structures using IVM observations, and found that sharp longitude gradients existed on a day-to-day basis.
 For IVM daytime E × B drift velocities to be useful, a number of constraints had to be imposed related to local time, altitude, and longitude [Araujo-Pradere et al., 2011]. The constraint on local time was to choose C/NOFS IVM E × B drift observations only between 10 and 13 LT. This insures that the E × B drifts are near their maximum daytime values so that sharp longitude gradients in E × B drift velocities are due to longitude effects and not due to local time changes. Since the chosen IVM observations were within ±15° magnetic latitude, and there is very little height gradient in daytime E × B drift velocities up to an apex height of 800 km [Pingree and Fejer, 1987], no magnetic latitude constraints needed to be applied to the data.
Figure 1, taken from Araujo-Pradere et al. , depicts the IVM-observedE × B drift velocity gradient in the Eastern Pacific sector between ∼240° and 265° E. longitude for 3 consecutive days on 19, 20, and 21 March 2009. For these 3 days the slopes in the gradients are roughly +3 m/s/deg. The altitude and magnetic latitude changes are from 405 km to 450 km and −1° to 11°, respectively. Figure (right), from Scherliess et al. , clearly demonstrates that the boundary of the Eastern Pacific sector cell is being observed in going from ∼240° to 250° E. longitude. The TEC observations in Figure 1 were normalized to a common baseline as described by Scherliess et al. .
 In this paper, we incorporate the sharp longitude gradients in E × Bdrift velocities into the time-dependent, theoretical, Global Ionosphere Plasmasphere (GIP) model and calculate ion densities as a function of altitude, latitude, longitude and local time for the particular days and longitude sectors being studied.
 This paper presents new, unique theoretically calculated ionospheric parameters that can be compared and validated with a variety of observations that are important and of interest to the navigation community. The response of the ionosphere to the sharp longitude gradients in E × B drift velocities is directly relevant to navigation customers in the equatorial region who are interested in developing a Wide Area Augmentation System (WAAS) in Brazil and India. In a recent talk by Dr. T. Walter of Stanford University (http://waas.stanford.edu) at the Second LISN (Low-latitude Ionospheric Sensor Network) Workshop (Brazil, October 2011), entitled “Ionospheric Studies Required to Support GNSS Use by Aviation in Equatorial Areas,” he specifically stated the main purpose of the presentation was to “Identify ionospheric properties that must be better understood for GNSS use by aviation in equatorial areas.” The steepness of the longitude gradients in TEC critically affects the operational usefulness of these systems. The theoretical modeling results presented in this paper directly addresses navigation customer concerns.
 Furthermore, in a future study, a state-of-the-art, theoretical model will determine whether such sharp longitude gradients inE × B drift velocities can be calculated. If they can, then the results will be analyzed to determine the causes of the sharp gradients and their longitude dependence. Fuller-Rowell et al.  have described the theoretical model, the Whole Atmosphere Model (WAM) – a General Circulation Model (GCM) – built on the U.S. National Weather Service (NWS) Global Forecast System (GFS), to demonstrate the impact of terrestrial weather on the upper atmosphere. In a separate study, Akmaev et al. demonstrated that WAM successfully produced diurnal and semidiurnal tidal structure in the neutral temperature at 100 km altitude that was in excellent agreement with the TIMED/SABER observations of these quantities. The WAM model will be coupled to the GIP model through a self-consistent, global electrodynamics solver that provides GIP with global electric fields as input.
2. Results and Discussion
 The Global Ionosphere Plasmasphere (GIP) model solves coupled equations of continuity, momentum and energy balance equations along the magnetic field line and calculates time-dependent ionospheric and plasmaspheric densities, temperatures, and velocities on a global, three-dimensional grid [Millward et al., 2007]. The horizontal resolution in the low-latitude region is about 1° in latitude and 4.5° in longitude. In altitude, it covers the whole plasmasphere and gives information from 100 km to higher than 20,000 km. The GIP is based on the ionosphere and plasmasphere part of the Coupled Thermosphere Ionosphere Plasmasphere model (CTIP) [Millward et al., 2001]. In the CTIP, the ionospheric component is solved along geomagnetic field lines based on the offset dipole coordinate. While effective up to a point, the dipole is an incomplete description for the actual terrestrial field. This leads to serious inaccuracies, most notably in the equatorial American and the South Atlantic sectors where the magnetic field deviates strongly from a dipole. To move beyond this dipole description, GIP utilizes a Magnetic Apex coordinate system [Richmond, 1995] in which a global three-dimensional grid of magnetic field lines are created by tracing through the full International Geomagnetic Reference Field (IGRF). The resulting global grid contains all of the correct distortions and anomalies that characterize the actual terrestrial field. The low-latitude ionosphere where most plasma phenomena are controlled by the configuration of Earth's magnetic field is greatly improved by using the more realistic magnetic coordinates [Richmond, 1995]. The GIP model consists of a low-latitude and midlatitude region where interhemispheric transport along flux tubes is taken into account and a high-latitude portion where no plasma flows across an upper boundary of 10000 km. The modular construction allows for GIP to be easily coupled to any kind of external neutral atmospheric models. In this study, the horizontal neutral wind from the Horizontal Wind Model (HWM-93) [Hedin et al., 1996] and thermospheric parameters (densities and temperature) from the Naval Research Laboratory Mass Spectrometer Incoherent Scatter Radar model (NRLMSISE-00) [Picone et al., 2002] are used to drive the GIP. The equatorial vertical drift is derived from the IVM observation.
 In order to study the effects of sharp longitude gradients in vertical E × B drift velocities on ionospheric electron and ion densities, we have chosen two specific days, 23 March and 7 October 2009, where IVM E × B drift velocities were obtained at the boundary between the Peruvian longitude sector and the Atlantic sector. For both days, the local times of the IVM observations run from 10:00 LT to 13:00 LT. Figure 2a presents IVM observations for 23 March where there is a sharp decrease in E × B drift velocity between 285° and 300° E. geographic longitude, going from 55 m/s to 10 m/s over this 15° segment. This amounts to a −3 m/s/deg gradient. Figure 2b presents IVM observations for 7 October where there is a sharp increase in E × B drift velocity between 300° and 337° E. geographic longitude. The velocity increases from −10 m/s to 40 m/s over this interval for an E × B drift gradient of +1.3 m/s/deg. Both of these days are extremely quiet with daily Ap values of 3 and 2 and an F10.7 cm flux value of 69 for both days.
 The observed vertical drifts are larger than the values derived from the climatological drift model [Scherliess and Fejer, 1999]. Therefore, the climatological drifts are multiplied by 1.5 to drive the GIP. Even though the C/NOFS IVM E × B drift velocities measured on 23 March 2009 near 280° longitude and on 7 October 2009 near 340° longitude seem somewhat higher than average, it is not the intent in this paper to go into details of the ongoing IVM validation efforts. We simply accept these values and have adjusted the Scherliess and Fejer climatological model to match the higher daytime E × B values to avoid discontinuities near 280° and 340° longitudes.
 The first set of ion density calculations assumed the absence of any sharp longitude gradients in E × B drift velocity. The E × B drift model is termed the Scherliess and Fejer control run (SF control) and the calculated ion densities at 400 km and 1400 LT are pictured in Figure 3a.
 In order to calculate ion densities as a function of altitude, latitude, longitude and local time, that reflect the sharp longitude gradients in E × B drifts pictured in Figures 2a and 2b, the Scherliess and Fejer E × B drift velocities times 1.5 (SF control) are chosen to represent the E × B drift inputs to the GIP model outside of the geographic longitude region between 285 and 340° E. longitude. Between 285 and 300° longitude, the SF control drifts are reduced by −3 m/s/deg from 55 m/s to 10 m/s. From 300° to 337° longitude, the E × B drifts are increased from −10 m/s to 40 m/s. These E × B drift changes are implemented after 0800 local time at all longitudes between 285 and 337°.
 Note that the crests of the equatorial anomaly in Figure 3a are roughly symmetric about the geomagnetic equator as the magnetic equator moves northward in going from the Peruvian to the Atlantic longitude sectors. The crests are located at roughly ±15° magnetic latitude and are the result of the daytime, upward E × B drift velocity that is incorporated into the GIP model. In the absence of upward E × B drift, the equatorial anomaly crests do not form [Hanson and Moffett, 1966]. This dependence of crest formation on the magnitude of upward E × B drift velocity is clearly demonstrated in Figure 3b. At 280° geographic longitude, the anomaly is well formed and the crests are located at ±15° magnetic latitude. As the longitude changes from 280° to 300°, the crests are located closer and closer to the magnetic equator because the daytime E × B drift velocity is decreasing dramatically as pictured in Figure 2a. Essentially, the equatorial anomaly disappears between 300° and 305° longitude. Eastward of 305° the crests begin moving away from the magnetic equator because the E × B drift velocity is increasing as pictured in Figure 2b. By 337° longitude, the crests are located at ±15° magnetic latitude. In essence, the steeper the longitude gradient in E × B drift, the steeper the longitude gradient in the equatorial anomaly crest location.
3. Summary and Future Work
 The Global Ionosphere Plasmasphere (GIP) theoretical, time-dependent ionospheric model was used to calculate ion densities as a function of altitude, latitude, longitude and local time. Incorporating theScherliess and Fejer  climatological E × Bdrift model (×1.5), the calculated ion density crests at 400 km and 1400 LT are roughly symmetric about the magnetic equator at ±17° magnetic latitude between 280° and 340° E. geographic longitude. Incorporating the IVM-observedE × B drift velocities, the ion density crests rapidly converge to the magnetic equator between 285° and 300°, are absent between 300° and 305° and move away from the magnetic equator between 305° and 340°. The convergence roughly matches the E × B drift longitude gradient in the Peruvian sector, while the divergence roughly matches the E × B drift longitude gradient in the Atlantic sector.
 The results presented here are unique theoretically calculated ionospheric parameters that can be compared and validated with a variety of observations that are important and of interest to the navigation community. The steepness of the longitude gradients in TEC critically affects the operational usefulness of these systems. The theoretical modeling results presented in this paper directly addresses navigation customer concerns. Furthermore, in a future study, a state-of-the-art, theoretical model will determine whether such sharp longitude gradients inE × B drift velocities can be calculated. If they can, then the model results can be analyzed to determine the causes of the sharp gradients and their longitude dependence.
 The C/NOFS mission is supported by the Air Force Research Laboratory, the Department of Defense Space Test Program, NASA, the Naval Research Laboratory, and the Aerospace Corporation. At the University of Colorado, this work is supported by AFOSR grant FA9550-09-0408. This work is supported at the University of Texas at Dallas by NASA grant NAS5-01068.